Question

compute the limit. if does not exist, explain:
lim f(x)...

Answer 1

\[\lim_{x \rightarrow \infty} 2x ^{2}-3x / 1-2x-3x ^{2}\]

Answer 2

multiply top and bottom by 1/x^2

Answer 3

so lim[ 2x^2/x^2 -3x / (2x^2) ]/ [ 1 /x^2 -2x/x^2 - 3x/x^2]

Answer 4

A type of L'Hopital application: infinity/infinity

First derivation step:

(4x-3) / (-2-6x) still infinity/infinity

Second step:

4 / (-6) = -2/3

This is the solution.
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